We discuss the weak star fixed point property in dual Banach spaces. We investigate the the existence of ergodic retractions in dual Banach spaces. We investigate the existence of ergodic retractions in dual Banach spaces. Recall that a a Banach space X has the fixed point property if, for every nonempty closed bounded convex subset C of X, every nonexpansive mapping of C into itself has a fixed point. A Banach space is said to have the weak fixed point property if the class of sets C above is restricted to the weakly compact convex sets; and a Banach space is said to have the weak* fixed point property if X is a dual space and the class of sets C is restricted to the weak* compact convex subsets of X
